# An integrated approach to grey relational analysis, analytic hierarchy process and data envelopment analysis

## TL;DR

This paper introduces an integrated multi-attribute decision-making approach combining grey relational analysis, analytic hierarchy process, and data envelopment analysis to evaluate alternatives with unknown attribute weights and fuzzy data.

## Contribution

It develops a novel methodology that integrates AHP and DEA within a fuzzy GRA framework to improve performance assessment accuracy.

## Key findings

- Provides a comprehensive performance measure for alternatives.
- Demonstrates effectiveness through nuclear waste site selection example.
- Overcomes limitations of traditional attribute weighting schemes.

## Abstract

Purpose: This paper aims to propose an integration of the analytic hierarchy process (AHP) and data envelopment analysis (DEA) methods in a multiattribute grey relational analysis (GRA) methodology in which the attribute weights are completely unknown and the attribute values take the form of fuzzy numbers. Design/methodology/approach: This research has been organized to proceed along the following steps: computing the grey relational coefficients for alternatives with respect to each attribute using a fuzzy GRA methodology. Grey relational coefficients provide the required (output) data for additive DEA models; computing the priority weights of attributes using the AHP method to impose weight bounds on attribute weights in additive DEA models; computing grey relational grades using a pair of additive DEA models to assess the performance of each alternative from the optimistic and pessimistic perspectives; and combining the optimistic and pessimistic grey relational grades using a compromise grade to assess the overall performance of each alternative. Findings: The proposed approach provides a more reasonable and encompassing measure of performance, based on which the overall ranking position of alternatives is obtained. An illustrated example of a nuclear waste dump site selection is used to highlight the usefulness of the proposed approach. Originality/value: This research is a step forward to overcome the current shortcomings in the weighting schemes of attributes in a fuzzy multiattribute GRA methodology. Keywords: Data envelopment analysis, Grey relational analysis, Analytic hierarchy process, Multiple attribute decision making, Fuzzy numbers, Weighting.

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Source: https://tomesphere.com/paper/1701.08890